\section{What remains to prove}
The organization now separates three questions. The address bijection
settles coverage of configurations. Fixed-degree ordering and the two
collision windows restrict equality of maxima. Complete residue witnesses
settle the remaining comparisons for the degree-bounded family in
Theorem~\ref{thm:degreebound}. The new computation compares more than 1.1 trillion configurations and
excludes every competitor for the first one trillion values in numerical
order. Meridian analysis helped turn the growth of related addresses
into a plan for comparing values by scale. The production implementation
uses certified Farey-cone bounds, compact residues, and cleared magnitude
bands, with 23.956 hours of retained active processing and a 0.992-GiB
recorded temporary key-file peak. These measurements describe the combined
algorithm and implementation; they do not measure the contribution of
Meridian coordinates in isolation. The numerical-prefix certificate can
be stated and checked without the Meridian collision theorems.

For unrestricted unicity the unresolved pair has different Meridian
degrees, the same modulo-27 class, and different Farey numerators.
It must satisfy both its phase rectangle and its numerator--denominator
window. A proof must exclude those candidates uniformly as the degrees
and numerators grow. Enlarging a finite certificate alone does not supply
that step. Likewise, an invertible corridor recurrence or a long modular
period does not by itself prevent an earlier match of one scalar residue.

Corridors offer a way to formulate the next comparison with explicit
entrance states and independently chosen wall lengths. Their positive
corrections are exact and telescope; the common-prefix snake calculation
offers a different reduction to a quadratic in primitive counts.
Neither mechanism has yet been shown to cover every unrestricted pair.
The purpose of retaining their precise hypotheses is to make the remaining
uniform statement identifiable, rather than hide it inside an induction.

\subsection*{Data and code}
The editable source accompanying this edition includes all figure assets,
the catenary, landscape, and Farey-grouping figure generators, a source and figure inventory, and checks
used for this rewrite. The separate degree reproducibility package contains
the full computational evidence cited in Section~\ref{sec:certificate}.
The new run's final evidence, resource reconciliation, and read-only
release checks are included with the source. Its frozen recovery archive
contains the complete retained receipt chain, candidate identities,
executables, source hashes, and independent checker \cite{TrillionVerification,BandVerification}.
The earlier fifty-billion proof and timing supplement remains a dated
historical companion; its full frozen archive is cited separately
\cite{Verification,FiftySupplement}.
The corridor derivations are developed further in the supplementary
research record \cite{CorridorRecord}. Numerical drawings are explanatory;
the arithmetic claims use the displayed identities or complete certificates.

\subsection*{Funding and competing interests}
No funding was received. The author declares no competing interests.